Ebook: The Fluid Dynamic Basis for Actuator Disc and Rotor Theories

loading...

Published

2018

Authors

Gijs van Kuik

ISBN

978-1-61499-865-5 (print) | 978-1-61499-866-2 (online)

Open Access

Description

The first rotor performance predictions were published by Joukowsky exactly 100 years ago. Although a century of research has expanded the knowledge of rotor aerodynamics enormously, and modern computer power and measurement techniques now enable detailed analyses that were previously out of reach, the concepts proposed by Froude, Betz, Joukowsky and Glauert for modelling a rotor in performance calculations are still in use today, albeit with modifications and expansions.

This book is the result of the author's curiosity as to whether a return to these models with a combination of mathematics, dedicated computations and wind tunnel experiments could yield more physical insight and answer some of the old questions still waiting to be resolved. Although most of the work included here has been published previously, the book connects the various topics, linking them in a coherent storyline. This book will be of interest to those working in all branches of rotor aerodynamics – wind turbines, propellers, ship screws and helicopter rotors. It has been written for proficient students and researchers, and reading it will demand a good knowledge of inviscid (fluid) mechanics.

Jens Nørkær Sørensen, DTU, Technical University of Denmark: “(…) a great piece of work, which in a consistent way highlights many of the items that the author has worked on through the years. All in all, an impressive contribution to the classical work on propellers/wind turbines.”

Carlos Simão Ferreira, Technical University Delft: “This is a timely book for a new generation of rotor aerodynamicists from wind turbines to drones and personal air-vehicles. In a time where fast numerical solutions for aerodynamic design are increasingly available, a clear theoretical and fundamental formulation of the rotor-wake problem will help professionals to evaluate the validity of their design problem. ‘The Fluid Dynamic Basis for Actuator Disc and Rotor Theories’ is a pleasure to read, while the structure, text and figures are just as elegant as the theory presented.”

It is exactly 100 years ago that prof. Joukowsky, one of the founders of modern aerodynamics, published the first rotor performance prediction. The tools of Joukowsky and his contemporaries were mathematics and wind tunnel experiments, nowadays we use mathematics, numerics, full scale experiments and, still, wind tunnel experiments. A century of research has expanded the knowledge of rotor aerodynamics enormously, with modern computer power and measurement techniques enabling detailed analyses of flows which were out of reach 100 years ago. However, the concepts for modelling a rotor in performance calculations as proposed by Froude, Betz, Joukowsky and Glauert are still used, be it with modifications and expansions. Especially the fast development of wind energy has revitalised the use of these concepts as they enable fast and accurate rotor designs.

Although the early models for a rotor have a proven track record, there is room for improvement in knowledge. The author returned to these models expecting that the combination of mathematics, dedicated computations and wind tunnel experiments would bring more physical insight. Furthermore, to the author's opinion several old questions were still waiting to be resolved. The result of this curiosity driven work is this book. Although most work has been published in papers, the book adds a storyline and connects topics. When the research started, there was not a storyline at all, only questions. None of the hours spent by the author has been part of any official R&D project as it would have been impossible to define objectives, deliverables or deadlines.

Although numerical methods and experiments have contributed to the book, most of the content is a mathematical treatment of the fluid dynamic aspects of rotor modelling as, quoting Maxwell (1831–1879): ‘there is nothing more practical than a good theory’.

see http://listverse.com/2009/02/26/another-10-most-influential-scientists/, last visited April 25, 2018. The quote is sometimes attributed to social psychologist Lewin (1890–1947) but he lived after Maxwell.

A good knowledge of (inviscid) fluid mechanics is required to read the book, which is written for proficient students and researchers.

Finally: on average the name of Joukowsky appears once per page, as his concept for an ideal rotor is examined in detail. The book is published one century after his first power prediction for a propeller in still air, a ship screw in still water or a hovering helicopter rotor, so it is dedicated to prof. Nikolay Yegorovich Joukowsky.

Reading guide

The book intends to be interesting for all branches in rotor aerodynamics: wind turbines, propellers, ship screws, helicopter rotors. However, with the background of the author in wind energy, many references relate to the wind turbine field of science. Chapter 1 treats the historical context, gives the motivation of the book and formulates several research questions. Chapters 2 and 3 are best read together, as they treat the advantage of the dynamic method (force fields as input in the equations of motion) over the kinematic method (force fields determined once the flow is solved), with emphasis on the two phenomena governing the flow: conversion of energy, and generation or conservation of vorticity. Chapter 4 shows why the actuator disc concept still is the correct basis for rotor design and analysis. The performance prediction by actuator disc theory is the topic of chapters 5 and 6: in 5 the disc concept conceived by Froude (no torque, no angular momentum in the wake) and in 6 the concept by Joukowsky (with torque and angular momentum). Both analyses are complemented by results of potential flow calculations. As a side step chapter 7 treats two special topics: the role for conservative forces acting on a disc with thickness, and on a rotor blade with non-zero chord and thickness. Chapter 8 is a chapter with an open end. Herein some results of previous chapters are combined to explore improvements in rotor design and analysis methods. Finally chapter 9 looks back.

The book is not written as a summation of independent chapters but follows a certain storyline. There is no forward referencing but quite some backward referencing. Chapters may be read apart from the others when these referenced equations and results are accepted, but it is advised to begin at the beginning and end at the end.